Spaces of D L p type and a convolution product associated with the spherical mean operator

M. Dziri, M. Jelassi and L. T. Rachdi

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-25

Abstract:

We define and study the spaces ℳ p ( ℝ × ℝ n ) , 1 ≤ p ≤ ∞ , that are of D L p type. Using the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual space ℳ ′ p ( ℝ × ℝ n ) and describe its bounded subsets. Next, we define a convolution product in ℳ ′ p ( ℝ × ℝ n ) × M r ( ℝ × ℝ n ) , 1 ≤ r ≤ p < ∞ , and prove some new results.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:529182

DOI: 10.1155/IJMMS.2005.357

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